Question

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"A" and "B" can complete a piece of work 24 days & 36 days respectively .
They start the work but, three(3) days before completion of work , "A" left .
How many days will the total work be completed ?
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Answer 1

Given :-

• A can complete work in 24 days .

• B can complete work in 36 days.

• A left work 3 days before it's completion .

To find :-

• Number of days in which the entire work will be completed.

Solution :-

We are provided with the capacity of both workers A and B that they can complete the work alone in how many days.

Firstly we'll find the working capicity of each worker in a single day .

→ A can complete work = 24 days

→ In one day A can complete part of work = $\frac{1}{24}$

→ B can complete work = 36 days

→ In one day B can complete part of work = $\frac{1}{36}$

Now we'll find how much units of work has to be completed ( Total work units ) .

By Finding the LCM of working capacity of each worker .

→ Total work = LCM of 24 and 36 is 72.

→ So total units of work is 72.

Now we'll find that each worker can complete how many units of work in every single day.

→ A can complete units of work = $\frac{72}{24} = 3$

→ A can complete 3 units per day .

→ B can complete Units of work = $\frac{72}{36} = 2$

→ So B can complete 2 units per day .

As its given that A left the work 3 days before it's completion .

Then we can say that the work that A will complete if he stays 3 days more now will be completed by B .

→ Work completed by A in 3 days = 3×3

→ So 9 units are added in the total work units .

→ Total work = 72 + 9 = 81 .

→ Work done by (A+B) = Total work units/Total units of work done by both workers per Day.

→ Work done by A+B = $\frac{81}{3+2}$

→ Work done = $\frac{81}{5} = 16.2$

Hence the work will be completed in 16.2 days

Answer 2

Step-by-step explanation:

We are provided with the capacity of both workers A and B that they can complete the work alone in how many days.

Firstly we'll find the working capicity of each worker in a single day .

→ A can complete work = 24 days

→ In one day A can complete part of work =

→ B can complete work = 36 days

→ In one day B can complete part of work =

Now we'll find how much units of work has to be completed ( Total work units ) .

By Finding the LCM of working capacity of each worker .

→ Total work = LCM of 24 and 36 is 72.

→ So total units of work is 72.

Now we'll find that each worker can complete how many units of work in every single day.

→ A can complete units of work = 3

→ A can complete 3 units per day .

→ B can complete Units of work = 2

→ So B can complete 2 units per day .

As its given that A left the work 3 days before it's completion .

Then we can say that the work that A will complete if he stays 3 days more now will be completed by B .

→ Work completed by A in 3 days = 3×3

→ So 9 units are added in the total work units .

→ Total work = 72 + 9 = 81 .

→ Work done by (A+B) = Total work units/Total units of work done by both workers per Day.

→ Work done by A+B = 81 / 3+2

→ Work done = 16.2

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